Abstract

In this paper, a simplified mathematical ray-optics model for an oil immersion objective lens, considering Abbe’s sine condition, is presented. Based on the given parameters of the objective lens, the proposed model utilizes an approach based on a paraxial thin lens formulation. This is done to simplify the complexity of the objective lens by avoiding the consideration of many lens elements inside a single objective lens. To demonstrate the performance of the proposed model, comparisons with exact ray tracing method, based on the specification of real objective lens, are presented in terms of several different criteria including the variation of shape of the light cone, the extent of vignetting and the focus displacement. From the exemplary simulations, it was demonstrated that the proposed model can describe the focusing of light through the objective lens precisely, even when the incident beam rotates.

© 2008 Optical Society of America

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References

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  1. O. Haeberlé, "Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part I: Conventional microscopy," Optics Commun. 216, 55-63 (2003).
    [CrossRef]
  2. M. Leutenegger, R. Rao, R. A. Leitgeb, and T. Lasser, "Fast focus field calculations," Opt. Express 14, 11277-11291 (2006).
    [CrossRef] [PubMed]
  3. I Bruce, "ABCD transfer matrices and paraxial ray tracing for elliptic and hyperbolic lenses and mirrors," Eur. J. Physiol. 27, 393-406 (2006).
  4. F. Pedrotti and L. Pedrotti, Introduction to Optics (Prentice Hall, 1993), Chap. 4, Chap. 6.
  5. R. E. Fischer, Optical System Design (McGraw-Hill, 2008).
  6. E. Fallman and O. Axner, "Design for fully steerable dual-trap optical tweezers," Appl. Opt. 36, 2107-2113 (1997).
    [CrossRef] [PubMed]
  7. C. Mio, T. Gong, A. Terray, and D. W. M. Marr, "Design of a scanning laser optical trap for multi-particle manipulation," Rev. Sci. Instrum. 71, 2196-2200 (2000).
    [CrossRef]
  8. S.-U. Hwang and Y.-G. Lee, "Maximizing the workspace of optical tweezers," J. Opt. Soc. Korea 11, 162-172 (2007).
    [CrossRef]
  9. M. Mansuripur, Classical Optics and Its Applications (Cambridge University Press, 2000), Chap. 1.
  10. M. Gu, P. C. Ke, and X. S. Gan, "Trapping force by a high numerical-aperture microscope objective obeying the sine condition," Rev. Sci. Instrum. 68, 3666-3668 (1997).
    [CrossRef]
  11. W. J. Smith, Modern Optical Engineering (McGraw-Hill, 2000), Chap. 13.
  12. R. Juškaitis, "Characterizing high numerical aperture microscope objective lens lenses," in Optical Imaging and Microscopy (Springer-Verlag, 2007).
  13. H. Y. Fujimoto and T. T. Kashara, "Immersion objective lens system for microscope," U.S. Patent 7199938B2 (2007).
  14. J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes, Computer graphics: Principles and practice in C (Addison-Wesley Professional, 1995), Chap. 16.
  15. M. Dinca and M. Pavelescu, "Caculus for a neutron imaging system based on a ccd camera," Rom. J. Phys. 51, 363-370 (2006).
  16. Y. Roichman, I. Cholis and D. G. Grier, "Volumetric imaging of holographic optical traps," Opt. Express 14, 10907-10912 (2006).
    [CrossRef] [PubMed]
  17. A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
    [CrossRef] [PubMed]
  18. R. Dorn, S. Quabis, and G. Leuchs, "The focus of light - linear polarization breaks the rotational symmetry of the focal spot," J. Mod. Opt. 50, 1917-1926 (2003).
  19. R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91, 233901 (2003).
    [CrossRef] [PubMed]
  20. N. Lindlein, S. Quabis, U. Peschel, and G. Leuchs, "High numerical aperture imaging with different polarization patterns," Opt. Express 15, 5827-5842 (2007).
    [CrossRef] [PubMed]

2007 (2)

2006 (4)

I Bruce, "ABCD transfer matrices and paraxial ray tracing for elliptic and hyperbolic lenses and mirrors," Eur. J. Physiol. 27, 393-406 (2006).

M. Dinca and M. Pavelescu, "Caculus for a neutron imaging system based on a ccd camera," Rom. J. Phys. 51, 363-370 (2006).

Y. Roichman, I. Cholis and D. G. Grier, "Volumetric imaging of holographic optical traps," Opt. Express 14, 10907-10912 (2006).
[CrossRef] [PubMed]

M. Leutenegger, R. Rao, R. A. Leitgeb, and T. Lasser, "Fast focus field calculations," Opt. Express 14, 11277-11291 (2006).
[CrossRef] [PubMed]

2003 (3)

R. Dorn, S. Quabis, and G. Leuchs, "The focus of light - linear polarization breaks the rotational symmetry of the focal spot," J. Mod. Opt. 50, 1917-1926 (2003).

R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

O. Haeberlé, "Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part I: Conventional microscopy," Optics Commun. 216, 55-63 (2003).
[CrossRef]

2000 (1)

C. Mio, T. Gong, A. Terray, and D. W. M. Marr, "Design of a scanning laser optical trap for multi-particle manipulation," Rev. Sci. Instrum. 71, 2196-2200 (2000).
[CrossRef]

1997 (2)

M. Gu, P. C. Ke, and X. S. Gan, "Trapping force by a high numerical-aperture microscope objective obeying the sine condition," Rev. Sci. Instrum. 68, 3666-3668 (1997).
[CrossRef]

E. Fallman and O. Axner, "Design for fully steerable dual-trap optical tweezers," Appl. Opt. 36, 2107-2113 (1997).
[CrossRef] [PubMed]

1992 (1)

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

Ashkin, A.

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

Axner, O.

Bruce, I

I Bruce, "ABCD transfer matrices and paraxial ray tracing for elliptic and hyperbolic lenses and mirrors," Eur. J. Physiol. 27, 393-406 (2006).

Cholis, I.

Dinca, M.

M. Dinca and M. Pavelescu, "Caculus for a neutron imaging system based on a ccd camera," Rom. J. Phys. 51, 363-370 (2006).

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, "The focus of light - linear polarization breaks the rotational symmetry of the focal spot," J. Mod. Opt. 50, 1917-1926 (2003).

R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Fallman, E.

Gan, X. S.

M. Gu, P. C. Ke, and X. S. Gan, "Trapping force by a high numerical-aperture microscope objective obeying the sine condition," Rev. Sci. Instrum. 68, 3666-3668 (1997).
[CrossRef]

Gong, T.

C. Mio, T. Gong, A. Terray, and D. W. M. Marr, "Design of a scanning laser optical trap for multi-particle manipulation," Rev. Sci. Instrum. 71, 2196-2200 (2000).
[CrossRef]

Grier, D. G.

Gu, M.

M. Gu, P. C. Ke, and X. S. Gan, "Trapping force by a high numerical-aperture microscope objective obeying the sine condition," Rev. Sci. Instrum. 68, 3666-3668 (1997).
[CrossRef]

Haeberlé, O.

O. Haeberlé, "Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part I: Conventional microscopy," Optics Commun. 216, 55-63 (2003).
[CrossRef]

Hwang, S.-U.

Ke, P. C.

M. Gu, P. C. Ke, and X. S. Gan, "Trapping force by a high numerical-aperture microscope objective obeying the sine condition," Rev. Sci. Instrum. 68, 3666-3668 (1997).
[CrossRef]

Lasser, T.

Lee, Y.-G.

Leitgeb, R. A.

Leuchs, G.

N. Lindlein, S. Quabis, U. Peschel, and G. Leuchs, "High numerical aperture imaging with different polarization patterns," Opt. Express 15, 5827-5842 (2007).
[CrossRef] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, "The focus of light - linear polarization breaks the rotational symmetry of the focal spot," J. Mod. Opt. 50, 1917-1926 (2003).

Leutenegger, M.

Lindlein, N.

Marr, D. W. M.

C. Mio, T. Gong, A. Terray, and D. W. M. Marr, "Design of a scanning laser optical trap for multi-particle manipulation," Rev. Sci. Instrum. 71, 2196-2200 (2000).
[CrossRef]

Mio, C.

C. Mio, T. Gong, A. Terray, and D. W. M. Marr, "Design of a scanning laser optical trap for multi-particle manipulation," Rev. Sci. Instrum. 71, 2196-2200 (2000).
[CrossRef]

Pavelescu, M.

M. Dinca and M. Pavelescu, "Caculus for a neutron imaging system based on a ccd camera," Rom. J. Phys. 51, 363-370 (2006).

Peschel, U.

Quabis, S.

N. Lindlein, S. Quabis, U. Peschel, and G. Leuchs, "High numerical aperture imaging with different polarization patterns," Opt. Express 15, 5827-5842 (2007).
[CrossRef] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, "The focus of light - linear polarization breaks the rotational symmetry of the focal spot," J. Mod. Opt. 50, 1917-1926 (2003).

R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Rao, R.

Roichman, Y.

Terray, A.

C. Mio, T. Gong, A. Terray, and D. W. M. Marr, "Design of a scanning laser optical trap for multi-particle manipulation," Rev. Sci. Instrum. 71, 2196-2200 (2000).
[CrossRef]

Appl. Opt. (1)

Biophys. J. (1)

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

Eur. J. Physiol. (1)

I Bruce, "ABCD transfer matrices and paraxial ray tracing for elliptic and hyperbolic lenses and mirrors," Eur. J. Physiol. 27, 393-406 (2006).

J. Mod. Opt. (1)

R. Dorn, S. Quabis, and G. Leuchs, "The focus of light - linear polarization breaks the rotational symmetry of the focal spot," J. Mod. Opt. 50, 1917-1926 (2003).

J. Opt. Soc. Korea (1)

Opt. Express (3)

Optics Commun. (1)

O. Haeberlé, "Focusing of light through a stratified medium: a practical approach for computing microscope point spread functions. Part I: Conventional microscopy," Optics Commun. 216, 55-63 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, "Sharper focus for a radially polarized light beam," Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (2)

C. Mio, T. Gong, A. Terray, and D. W. M. Marr, "Design of a scanning laser optical trap for multi-particle manipulation," Rev. Sci. Instrum. 71, 2196-2200 (2000).
[CrossRef]

M. Gu, P. C. Ke, and X. S. Gan, "Trapping force by a high numerical-aperture microscope objective obeying the sine condition," Rev. Sci. Instrum. 68, 3666-3668 (1997).
[CrossRef]

Rom. J. Phys. (1)

M. Dinca and M. Pavelescu, "Caculus for a neutron imaging system based on a ccd camera," Rom. J. Phys. 51, 363-370 (2006).

Other (7)

W. J. Smith, Modern Optical Engineering (McGraw-Hill, 2000), Chap. 13.

R. Juškaitis, "Characterizing high numerical aperture microscope objective lens lenses," in Optical Imaging and Microscopy (Springer-Verlag, 2007).

H. Y. Fujimoto and T. T. Kashara, "Immersion objective lens system for microscope," U.S. Patent 7199938B2 (2007).

J. D. Foley, A. van Dam, S. K. Feiner, and J. F. Hughes, Computer graphics: Principles and practice in C (Addison-Wesley Professional, 1995), Chap. 16.

M. Mansuripur, Classical Optics and Its Applications (Cambridge University Press, 2000), Chap. 1.

F. Pedrotti and L. Pedrotti, Introduction to Optics (Prentice Hall, 1993), Chap. 4, Chap. 6.

R. E. Fischer, Optical System Design (McGraw-Hill, 2008).

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Figures (11)

Fig. 1.
Fig. 1.

Simplified ray diagram of an infinity-corrected oil immersion objective lens. The rays leaving the front focal point F1, refract at the spherical refracting surface SS instead of classical principal plane PP1 in the paraxial regime.

Fig. 2.
Fig. 2.

Ray refraction by a paraxial thin lens

Fig. 3.
Fig. 3.

Ray trace modeling for infinity corrected oil immersion objective lens considering sine condition using paraxial thin lens

Fig. 4.
Fig. 4.

Schematic view of the incident beam propagating in parallel towards the objective lens along the positive z-axis

Fig. 5.
Fig. 5.

Results of the proposed ray tracing model, when implemented on the infinity-corrected oil immersion objective lens (Olympus, #UPLSAPO 100XO, 100x, f: 1.8 mm, NA: 1.4, WD: 0.13 µm, tg: 0.17 mm). (a) On-axis incident beam, (b) Rotation of on-axis incident beam around the center of the objective back aperture, (c) Off-axis incident beam (h: 0.5 mm).

Fig. 6.
Fig. 6.

Result of ray tracing based on real objective lens specifications (Olympus, 100x, f: 1.8 mm, NA: 1.41, WD: 0.13 µm, oil, tg: 0.17 mm), (a) On-axis incident beam, (b) Rotation of onaxis incident beam around the center of the objective back aperture to about 1.8 degrees, (c) Off-axis incident beam with an axis of 0.5 mm.

Fig. 7.
Fig. 7.

Deviation of the incident angle of a fan of rays from the surface normal at each refracting surface (a) On-axis incident beam, (b) Rotation of on-axis incident beam around the center of the objective back aperture to about 1.8 degrees, (c) Off-axis incident beam with a shift of 0.5 mm

Fig. 8.
Fig. 8.

Comparison of half cone angle errors between the proposed model and the exact ray tracing, and between the thin lens model and exact ray tracing when the incident beam rotates, using real objective lens specifications (100x, f: 1.8 mm, NA: 1.41, WD: 0.13 µm, oil, tg: 0.17 mm)

Fig. 9.
Fig. 9.

Comparison of half cone angle errors between the proposed model and the exact ray tracing with respect to off-axis distance (100x, f: 1.8 mm, NA: 1.41, WD: 0.13 µm, oil, tg: 0.17 mm). (a) Variation of half cone angle errors with off-axis distance, (b) Variation of left-half cone angle error for different off-axis distances when incident beam rotates, (b) Variation of right-half cone angle error for different off-axis distances when incident beam rotates

Fig. 10.
Fig. 10.

Comparison of the number of rays passing through objective back aperture for proposed model and exact ray tracing (100x, f: 1.8 mm, NA: 1.41, WD: 0.13 µm, oil, tg: 0.17 mm) when rotation center of incident beam is displaced from the back focal plane. (a) On-axis incident beam, (b) Off-axis incident beam (h: 0.25 mm), (c) Off-axis incident beam (h: 0.5 mm).

Fig. 11.
Fig. 11.

Focus displacement error between proposed model and exact ray tracing (100x, f: 1.8 mm, NA: 1.41, WD: 0.13 µm, oil, tg: 0.17 mm) when the incident beam rotates around the center of the objective back aperture.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

D = 2 nf · sin α = 2 f · NA .
r = i ̂ ρ cos ϕ f .
r = r r ̂ = ( f cos ϕ ) i ̂ ρ
r u = r + a = ( f cos ϕ ) i ̂ ρ + f ( n 1 ) z ̂ .
s = [ nf ( nf ) 2 ρ 2 ] i ̂
r o = r u s
= ( f cos ϕ nf + ( nf ) 2 ρ 2 ) i ̂ ρ + f ( n 1 ) z ̂
i ( t ) = P 1 + t i ̂ 1
P 1 = ( r cos θ , r sin θ , l )

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